A Polarity Theory for Sets of Desirable Gambles
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http://hdl.handle.net/10045/70568
Title: | A Polarity Theory for Sets of Desirable Gambles |
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Authors: | Benavoli, Alessio | Facchini, Alessandro | Zaffalon, Marco | Vicente-Pérez, José |
Research Group/s: | Desarrollo, Métodos Cuantitativos y Teoría Económica (DMCTE) | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Fundamentos del Análisis Económico |
Keywords: | Desirability | Credal sets | Lexicographic probabilities | Separation theorem | Polarity |
Knowledge Area: | Fundamentos del Análisis Económico |
Issue Date: | 2017 |
Publisher: | PMLR |
Citation: | Proceedings of Machine Learning Research. 2017, 62: 37-48 |
Abstract: | Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is based on the polarity theory for closed convex cones. Learning from this simple observation, in this paper we introduce a new (lexicographic) polarity theory for general convex cones and then we apply it in order to establish an analogous correspondence between coherent sets of desirable gambles and convex sets of lexicographic probabilities. |
Sponsor: | J. Vicente-Pérez was partially supported by MINECO of Spain and ERDF of EU, Grants MTM2014-59179-C2-1-P and ECO2016-77200-P. |
URI: | http://hdl.handle.net/10045/70568 |
ISSN: | 1938-7288 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © PMLR 2017 |
Peer Review: | si |
Publisher version: | http://proceedings.mlr.press/v62/benavoli17b.html |
Appears in Collections: | INV - DMCTE - Artículos de Revistas INV - LOPT - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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2017_Benavoli_PMLR.pdf | 217,1 kB | Adobe PDF | Open Preview | |
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